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Simplifying 55 = -16t2 + 62t + 3 Reorder the terms: 55 = 3 + 62t + -16t2 Solving 55 = 3 + 62t + -16t2 Solving for variable 't'. Combine like terms: 55 + -3 = 52 52 + -62t + 16t2 = 3 + 62t + -16t2 + -3 + -62t + 16t2 Reorder the terms: 52 + -62t + 16t2 = 3 + -3 + 62t + -62t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 52 + -62t + 16t2 = 0 + 62t + -62t + -16t2 + 16t2 52 + -62t + 16t2 = 62t + -62t + -16t2 + 16t2 Combine like terms: 62t + -62t = 0 52 + -62t + 16t2 = 0 + -16t2 + 16t2 52 + -62t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 52 + -62t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(26 + -31t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + -31t + 8t2)' equal to zero and attempt to solve: Simplifying 26 + -31t + 8t2 = 0 Solving 26 + -31t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.25 + -3.875t + t2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -3.875t + -3.25 + t2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -3.875t + t2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -3.875t + t2 = 0 + -3.25 -3.875t + t2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -3.875t + t2 = -3.25 The t term is -3.875t. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875t + 3.75390625 + t2 = -3.25 + 3.75390625 Reorder the terms: 3.75390625 + -3.875t + t2 = -3.25 + 3.75390625 Combine like terms: -3.25 + 3.75390625 = 0.50390625 3.75390625 + -3.875t + t2 = 0.50390625 Factor a perfect square on the left side: (t + -1.9375)(t + -1.9375) = 0.50390625 Calculate the square root of the right side: 0.709863543 Break this problem into two subproblems by setting (t + -1.9375) equal to 0.709863543 and -0.709863543.Subproblem 1
t + -1.9375 = 0.709863543 Simplifying t + -1.9375 = 0.709863543 Reorder the terms: -1.9375 + t = 0.709863543 Solving -1.9375 + t = 0.709863543 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = 0.709863543 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = 0.709863543 + 1.9375 t = 0.709863543 + 1.9375 Combine like terms: 0.709863543 + 1.9375 = 2.647363543 t = 2.647363543 Simplifying t = 2.647363543Subproblem 2
t + -1.9375 = -0.709863543 Simplifying t + -1.9375 = -0.709863543 Reorder the terms: -1.9375 + t = -0.709863543 Solving -1.9375 + t = -0.709863543 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = -0.709863543 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = -0.709863543 + 1.9375 t = -0.709863543 + 1.9375 Combine like terms: -0.709863543 + 1.9375 = 1.227636457 t = 1.227636457 Simplifying t = 1.227636457Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.647363543, 1.227636457}Solution
t = {2.647363543, 1.227636457}
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